Recently, it is becoming popular to project videos not only to a flat surface but also to a curved surface such as a column or a dome. There is proposed a projection apparatus having an image deformation function so as to prevent a viewer from sensing the distortion of a video when projecting videos to various projection surfaces. The projection apparatus projects an image deformed in accordance with the projection surface, and the viewer can observe a video from which their does not feel a distortion.
However, if an image deformation arithmetic circuit for projecting an image from which a viewer does not feel a distortion is mounted in the projection apparatus for each of the shapes of various projection surfaces such as a cylindrical shape and a hemispherical shape, the circuit scale of the projection apparatus increases.
As a method for solving this problem, there is known a method of storing, in a memory, the coordinate values of grid points arranged in a pre-deformation image, and associating the respective grid points with locations in a deformed image. There is also known a method of storing, in a memory, the coordinate values of grid points disposed in a deformed image, and associating the respective grid points with locations in a pre-deformation image.
By using this association and the pixel value of a pixel of interest in a pre-deformation image, the pixel value of a pixel of interest in a deformed image can be obtained. This method can implement common use of the image deformation function regardless of the shape of the projection surface.
In general, calculation of a pixel value in the image deformation function for the projection apparatus is performed by inverse transformation rearrangement in order to prevent a missing pixel. More specifically, each pixel of a deformed image is set as a pixel of interest, and a coordinate values (to be referred to as a “coordinate values before deformation” hereinafter) before deformation that corresponds to the coordinate values of the pixel of interest are obtained by coordinate transformation. Then, the value of the pixel of interest is calculated using the value of a pixel (to be referred to as a “pixel of interest before deformation”) corresponding to the coordinate values before deformation, and the values of pixels surrounding the pixel of interest before deformation.
As a method of obtaining a coordinate value before deformation, two methods are known: one is a method (to be referred to as a “post-deformation lattice method” hereinafter) using the coordinate values of grid points before deformation and the coordinate values of the grid points after deformation. The other is a method (to be referred to as a “pre-deformation lattice method” hereinafter) using the coordinate values of grid points after deformation and the inversely deformed coordinate values of the grid points before deformation.
International Publication No. 08/139577 (literature 1) discloses a pre-deformation lattice method in which transformed coordinate values (coordinate values before deformation) from those after deformation to those before deformation are stored in a memory as the coordinate values of grid points. According to the pre-deformation lattice method, in a deformation in which an image is reduced inward, grid points located outside the deformed image are located outside the deformed shape and become unnecessary. As a result, all grid points are not used for coordinate transformation, and the accuracy of coordinate transformation decreases. The decrease in the accuracy of coordinate transformation is a factor of image quality degradation such that, when deformed images are partially superposed to project the entire image at the time of, for example, combined projection by a plurality of projection apparatuses, displacement occurs between the deformed images, and as a result decreasing the sharpness of an image obtained by combining the deformed image.
Japanese Patent Laid-Open No. 2001-069434 (literature 2) discloses a post-deformation lattice method. The post-deformation lattice method requires a function of determining grid points to be used to calculate the coordinate values of a pixel of interest before deformation. In literature 2, coordinate values after deformation are used as the coordinate values of grid points, however any method of determining the grid points is not mentioned.